#rotational dynamics

PHYSICS

A uniform rod of mass 5 kg and length 2 m is pivoted at its nter. What is its moment of inertia about the pivot?

Given: A uniform rod of mass 5 kg and length 2 m is pivoted at its nter. What is its moment of inertia about the pivot? Formula: For a rod pivoted at its nter: I = 1/12 M L². Substitution & Calculation: M = 5 kg, L = 2 m . I = 1/12 × 5 × (2)² = 20/12 = 5/3 approx 1.67 kg m² . Final Result: The computed value matches expected outcome and confirms correct choice as per latest NCERT 2026-27.

Ref: NCERT Physics Textbook - Latest Edition for Academic Session 2026-27 (Rationalized Textbook for Class XI and XII, continuing as per NCERT advisory for 2026-27),Topic: Fundamental laws, definitions and applications as per latest NCERT. The section explains governing laws, formulas like μ₀ = 4π.

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PHYSICS

What is the effect of a force applied at the axis of rotation on a rigid body?

A force applied at the axis ( r = 0 ) produces no torque ( tau = r F sin θ = 0 ), so it cannot cause rotation about that axis. This follows from latest NCERT 2026-27 principle explaining the concept clearly for NEET students in simple steps as per rationalized syllabus.

Ref: NCERT Physics Textbook - Latest Edition for Academic Session 2026-27 (Rationalized Textbook for Class XI and XII, continuing as per NCERT advisory for 2026-27),Topic: Fundamental laws, definitions and applications as per latest NCERT. The section explains governing laws, formulas like μ₀ = 4π.

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PHYSICS

What is the effect of increasing the mass of a rotating body on its angular momentum, if angular velocity remains consta

Angular momentum L = I omega, and I increases with mass. If omega is constant, L increases proportionally with mass. This follows from latest NCERT 2026-27 principle explaining the concept clearly for NEET students in simple steps as per rationalized syllabus.

Ref: NCERT Physics Textbook - Latest Edition for Academic Session 2026-27 (Rationalized Textbook for Class XI and XII, continuing as per NCERT advisory for 2026-27),Topic: Fundamental laws, definitions and applications as per latest NCERT. The section explains governing laws, formulas like μ₀ = 4π.

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Vector Product and Rotational Kinematics

A wheel with moment of inertia 6kg m2 rotates at 3rad/s. A torque of 12Nm acts for 3s. What is its final angular velocit

α = τI = 126 = 2rad/s2. Δω = αt = 2×3 = 6rad/s. ω = ω0+Δω = 3+6 = 9rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Vector Product and Rotational Kinematics

A solid sphere of mass 5kg and radius 0.3m rotates about an axis through its center. If its angular momentum is 9kg m2/s

L = Iω. For a sphere: I = 25MR2 = 25×5×(0.3)2 = 0.18kg m2. ω = LI = 90.18 = 50rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 50 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Vector Product and Rotational Kinematics

Why does a symmetric body rotating about its symmetry axis have angular momentum aligned with the axis?

Symmetry ensures perpendicular components of angular momentum cancel out, leaving L = Iω aligned with the axis of rotation. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Due to cancellation of perpendicular components. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Rotational Motion Applications

A torque of 21Nm acts on a wheel with moment of inertia 7kg m2 starting from rest. What is its angular speed after 4s?

α = τI = 217 = 3rad/s2. ω = ω0+αt = 0+3×4 = 12rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 12 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Rotational Motion Applications

Which statement is true about the axis of rotation in pure rotational motion?

In pure rotational motion, the axis of rotation is fixed, meaning it does not move or change direction, constraining the body to rotate about it. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It is always fixed. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Rotational Motion Applications

A disk with moment of inertia 1.5kg m2 rotates at 4rad/s. A torque of 6Nm acts for 3s. What is its final angular velocit

α = τI = 61.5 = 4rad/s2. Δω = αt = 4×3 = 12rad/s. ω = ω0+Δω = 4+12 = 16rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 16 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Rotational Motion Applications

A wheel of radius 0.4m and moment of inertia 1.6kg m2 is accelerated by a torque of 8Nm. What is its angular acceleratio

Torque: τ = Iα. τ = 8Nm, I = 1.6kg m2. α = τI = 81.6 = 5rad/s2. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5 rad/s². This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Conservation of Angular Momentum

Why does a body with zero net torque maintain its rotational state?

Zero net torque (τ = 0) means no change in angular momentum (dLdt = 0), so the rotational state (angular velocity) remains constant. As per NCERT, applying relevant law/formula with correct units and sign convention leads to Due to no change in angular momentum. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Conservation of Angular Momentum

In rotational dynamics, what role does torque play?

Torque causes angular acceleration, as per τ = Iα, analogous to how force causes linear acceleration in Newton’s second law. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It causes angular acceleration. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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